Why does BODMAS work?

Question

In mathematic equations, we were taught to use bodmas (brackets, order, division, multiplication, addition, subtraction). so brackets come before division, division comes before multiplication, which comes before addition...etc.

Answer 1

Actually, multiplication and division can be done in which ever order you want. The same applies for addition and subtraction. So division does NOT come before multiplication, either way will yield the same result.

Okay, now that that is clear, the reason that you exponentiate (or log) before you do anything else. Then you do all the multiplication and divisions and then you do additions and subtractions, is simply convention. When we WRITE down a math expression, we follow conventions (they are arbitrary and could be different).

It is exactly the same when we use language. Take the three words: "Peter", "Paul" and "killed". We have conventions on how to order them to give a determined meaning. If you read "Paul killed Peter" it is clear that Paul was the subject of an action that involved Peter. In some other convention we might have to write "Peter killed Paul" or "Killed Paul Peter" or some other combination to mean the same thing.

So how do brakets or parenthesis come in play? They are "modifiers" of the exponential/log - multiplication/division - addition/subtraction order. In the example "Paul killed Peter", we can also use "modifiers". "Paul was killed by Peter" "was" and "by" completely change the diection of "killed".

Hope this helped.

Answer 2

It's partly a convention but also a natural ordering of the various operations... by the way, I learned it as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction), or "Please Excuse My Dear Aunt Sally", but it is the same thing.

It works because brackets (parentheses) have the highest precedence. They can "override" the natural precedence. After that is the order (exponent). Notice how 2^3 = 2 x 2 x 2, so this is sort of like a grouping of multiplication. Next comes multiplication and division (which have equal precendence; division is just multiplication inverted). This is why PEMDAS, BOMDAS, BODMAS, PEDMAS would all work. Notice again how 3x2 = 2+2+2, so it shows how multiplication is a grouping of addition. Finally you have addition and subtraction which have the lowest precedence. Again they have equivalent precedence since subtraction is just a negative addition, but we logically think of addition then subtraction though there is no reason you couldn't do the subtraction first.

So it is partly convention and partly the definition of brackets (parentheses), order (exponents), multiplication/division and addition/subtraction. But it is all logical, if you think about it.

Answer 3

a + sign comes before addition

Answer 4

Why does it work? Because we make it work. We need conventions in order to be able to evaluate mathematical expressions, so these are the rules that we invented.

Answer 5

It's PEDMAS, and it's merely another math rule so we all agree on the math and reach the same result.

Answer 6

isn't it


BOMDAS


brackets
of (multiply)
Multiply
Divide
Addition
Subtraction